Error Control of Phase-Function Shooting Methods for Sturm-Liouville Problems

A popular method for computing eigenvalues and eigenfunctionsof Sturm-Liouville systems is to convert to phase-amplitudevariables (, r) in the (y', y)- plane (a Prüer transformation)and solve the resulting equations by a shooting method usingan ODE initial-value code. We study the error control of suchmethods with specific reference to two published codes basedon this technique, and make comparisons and recommendations.Improved error estimates are derived and evidence for theirefficacy presented.